5 problems

Kubat–Okniński's conjecture. Every plactic monoid of finite rank satisfies a non-trivial semigroup identity.

Let $A$ be a finite ordered set, let $\Bbbk$ be a commutative unital ring, and let $\mathbf{Pl}_A$ denote the plactic monoid on $A$. Theorem gives an injective algebra map from the…

Finite-rank plactic identity conjecture. For each $n \geq 4$, there is a non-trivial identity satisfied by ${\mathsf{plac}}_n$.

Permutohedral conjecture. The generating $n$-cells of the resolution have the form of the permutohedron of order $n$ corresponding to a confluence diagram of $(n-1)$ overlapping re…

Let $a,b$ be the parameters defining the relevant Kazhdan–Lusztig cells, let $r\geq 1$, and let signed permutations lie in $B_n$. Two signed permutations are $r$-cycle equivalent (…